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About Multigrid Convergence of Some Length Estimators [chapter]

Loïc Mazo, Étienne Baudrier
2014 Lecture Notes in Computer Science  
An interesting property for curve length digital estimators is the convergence toward the continuous length and the associate convergence speed when the digitization step h tends to 0.  ...  On the other hand, DSS and MLP based estimators have been proved to converge but only under some convexity and smoothness or polygonal assumptions.  ...  h (below some threshold), the error between the estimated length L est (C, h) and the true length of the polygon L(C) is such that |L(S) − L est (S, h)| ≤ (2 + √ 2)πh. (1) Empirical MDSS multigrid convergence  ... 
doi:10.1007/978-3-319-09955-2_18 fatcat:hvwfz2ylx5c6xmdn5e5mxtfn5q

Parameter-Free and Multigrid Convergent Digital Curvature Estimators [chapter]

Jérémy Levallois, David Coeurjolly, Jacques-Olivier Lachaud
2014 Lecture Notes in Computer Science  
In this paper, we propose new variants of these estimators which are parameter-free and ensure multigrid convergence in 2D.  ...  Focusing on multigrid convergent estimators, most of them require a user specified parameter to define the scale at which the analysis is performed (size of a convolution kernel, size of local patches  ...  In dimension 3, there is no parameter-free estimator which provides some multigrid convergence.  ... 
doi:10.1007/978-3-319-09955-2_14 fatcat:2pxlp37smjbwjg4yqk3i7c5mna

Convex Shapes and Convergence Speed of Discrete Tangent Estimators [chapter]

Jacques-Olivier Lachaud, François de Vieilleville
2006 Lecture Notes in Computer Science  
We show that such estimators are multigrid convergent for some family of convex shapes and that their speed of convergence is on average O(h 2 3 ).  ...  This paper studies the multigrid convergence of tangent estimators based on maximal digital straight segment recognition.  ...  In this paper, we are mainly interested by the multigrid convergence property of some estimators, which is one of the few existing objective criteria.  ... 
doi:10.1007/11919629_69 fatcat:xyt4lzxpnrho7fcg2ixrmzqsge

Multigrid Convergence of Discrete Geometric Estimators [chapter]

David Coeurjolly, Jacques-Olivier Lachaud, Tristan Roussillon
2012 Lecture Notes in Computational Vision and Biomechanics  
We present here global geometric estimators of area, length, moments, as well as local geometric estimators of tangent and curvature.  ...  Known theorems on multigrid convergence are summarized.  ...  Global Estimators Multigrid convergence for global estimators Multigrid convergence is an interesting way of relating digital and Euclidean geometries.  ... 
doi:10.1007/978-94-007-4174-4_13 fatcat:ym22kbvxdfh35hz22yqe6yrbem

Multigrid-convergence of digital curvature estimators

Jacques-Olivier Lachaud
2013 Actes des rencontres du CIRM  
The problem is then: can we define curvature estimators that are multigrid convergent without such user-given parameter ? If so, what speed of convergence can we achieve ?  ...  A digital geometric estimator is called multigrid convergent whenever the estimated quantity tends towards the expected geometric quantity as the grid step gets finer and finer.  ...  Some of these notions are illustrated on Fig. 5 .1, right. Digital contour, multigrid convergence.  ... 
doi:10.5802/acirm.66 fatcat:b6dfpbsvpvbfvh5cniexxsh53m

Multigrid Convergent Curvature Estimator [chapter]

Christophe Fiorio, Christian Mercat, Frédéric Rieux
2013 Lecture Notes in Computer Science  
We study the bounded error of our approach for first and second order derivative and we discuss about the multigrid convergence.  ...  We propose in this paper an estimator of derivative and curvature of discrete curves.  ...  The issue of the length of the mask has not been studied in this paper and we have few information about the minimal length to have a satisfying estimation.  ... 
doi:10.1007/978-3-642-37067-0_34 fatcat:mqvvhq77kzaizedcmyt6sd5ffi

A comparative evaluation of length estimators of digital curves

D. Coeurjolly, R. Klette
2004 IEEE Transactions on Pattern Analysis and Machine Intelligence  
The evaluation uses multigrid convergence (theoretical results and measured speed of convergence) and further measures as criteria.  ...  This paper also suggests a new gradient-based method for length estimation, and combines a previously proposed length estimator for straight segments with a polygonalization method.  ...  Coeurjolly was a member of the ERIC Laboratory (Université Lumière Lyon 2).  ... 
doi:10.1109/tpami.2004.1262194 pmid:15376899 fatcat:psisn6pwwnhofoyvcxyaamjpcu

An adaptive multigrid technique for the incompressible Navier-Stokes equations

M.C. Thompson, J.H. Ferziger
1989 Journal of Computational Physics  
For driven cavity flow at Re = 1000, the adaptive refinement approach reduced the computer memory and CPU time to 20 and 40% of the requirements of the "pure" multigrid method.  ...  The primitive-variable formulation of the Navier-Stokes equations is used so the method can be extended easily to three dimensions.  ...  Caruso who kindly provided a version of his adaptive grid code as a starting  ... 
doi:10.1016/0021-9991(89)90037-5 fatcat:dgtennownjgpfbrhhln63pi234

A Comparison of Property Estimators in Stereology and Digital Geometry [chapter]

Yuman Huang, Reinhard Klette
2004 Lecture Notes in Computer Science  
We evaluate common estimators in stereology and digital geometry according to their multiprobe or multigrid convergence properties, and precision and efficiency of estimations.  ...  We consider selected geometric properties of 2D or 3D sets, given in form of binary digital pictures, and discuss their estimation.  ...  Acknowledgement: The authors thank the reviewers of IWCIA for their valuable comments.  ... 
doi:10.1007/978-3-540-30503-3_30 fatcat:hv2q6vqhtreblm7ihstkuxknqu

A Comparative Study on 2D Curvature Estimators

Simon Hermann, Reinhard Klette
2007 2007 International Conference on Computing: Theory and Applications (ICCTA'07)  
Results of multigrid experiments are evaluated leading to a comparative performance analysis of several curvature estimators.  ...  This paper presents curvature estimators which follow approaches in differential geometry. Digital-straight segment approximation (as known from digital geometry) is used in those estimators.  ...  Discussion Applying the DSS approach for curvature estimators does not seem to guarantee multigrid convergence (in difference to DSS-based multigrid convergent length estimation).  ... 
doi:10.1109/iccta.2007.2 dblp:conf/iccta/HermannK07 fatcat:a4shahrrynekjisky7aejuun7a

Page 1633 of Mathematical Reviews Vol. , Issue 83d [page]

1983 Mathematical Reviews  
In the worst situation, both the storage and the computational work are only about a factor of two more than the unmodified multigrid methods.”  ...  In principle, this new multigrid algorithm converges for elliptic systems arbitrarily close to a singularity and it has been used successfully in conjunction with arc-length continuation procedures on  ... 

Another Look at Neural Multigrid

Martin Bäker
1997 International Journal of Modern Physics C  
In the case of the two-dimensional Laplace equation with SU(2) gauge fields at beta=0 the learning exhibits critical slowing down with an exponent of about z = 0.4.  ...  We present a new multigrid method called neural multigrid which is based on joining multigrid ideas with concepts from neural nets.  ...  Acknowledgments I wish to thank Daniel L ubbert for rekindling my i n terest in neural multigrid. Financial support by Deutsche Forschungsgemeinschaft is gratefully acknowledged.  ... 
doi:10.1142/s0129183197000187 fatcat:5uzkfzerqvd7lca3d5yebrak3i

Robust and Convergent Curvature and Normal Estimators with Digital Integral Invariants [chapter]

Jacques-Olivier Lachaud, David Coeurjolly, Jérémy Levallois
2017 Lecture notes in mathematics  
During the course of the chapter, we establish several multigrid convergence results of digital volume and moments estimators in arbitrary dimensions.  ...  We show the multigrid convergence of all these estimators, which means that their estimations tend toward the exact geometric quantities onsmooth enough-Euclidean shapes digitized with finer and finer  ...  multigrid convergence is that when we define a quantity estimator on the digitization of some shape X ⇢ R d , we check if the estimated quantity converges (theoretically and/or experimentally) to the  ... 
doi:10.1007/978-3-319-58002-9_9 fatcat:lukbsriyjjgy7nngkg37pwnjdq

A Multigrid Algorithm for Sampling Imaginary-Time Paths in Quantum Monte Carlo Simulations [article]

C.H. Mak, Sergei Zakharov
2004 arXiv   pre-print
This method combines a stochastic blocking procedure with the multigrid method to rapidly accelerate the sampling of paths in a quantum Monte Carlo simulation, making its dynamics more ergodic.  ...  We describe a novel simulation method that eliminates the slowing-down problem in the Monte Carlo simulations of imaginary-time path integrals near the continuum limit.  ...  The real efficiency of the multigrid method at the minimum required discretization for convergence (L = 5) is about a factor of 4 better than its nearest competitor, the bisection method, and a factor  ... 
arXiv:cond-mat/0402181v1 fatcat:7zutyilfrbf6znqd2lnabunama

Multigrid-in-time for sensitivity analysis of chaotic dynamical systems [article]

Patrick Blonigan, Qiqi Wang
2013 arXiv   pre-print
Several different multigrid-in-time schemes are examined, and a number of factors were found to heavily influence the convergence rate of multigrid-in-time for LSS.  ...  Multigrid is used because LSS requires solving a very large Karush-Kuhn-Tucker (KKT) system constructed from the solution of the dynamical system over the entire time interval of interest.  ...  Figure 20 shows that the solution of the KKT system converges after about 4700 iterations, and the gradient converges after about 1800 iterations.  ... 
arXiv:1305.6878v2 fatcat:lha6axgtwbea5e44lsb6s7apdu
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